Equivalents of the finitary non-deterministic inductive definitions

Ayana Hirata; Hajime Ishihara; Tatsuji Kawai; Takako Nemoto

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arXiv · 1903.05852

Equivalents of the finitary non-deterministic inductive definitions

Ayana Hirata·Hajime Ishihara·Tatsuji Kawai·Takako Nemoto

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Abstract

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID.

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Ayana Hirata, Hajime Ishihara, Tatsuji Kawai, Takako Nemoto. 2019-03-14. Equivalents of the finitary non-deterministic inductive definitions. https://arxiv.org/abs/1903.05852

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